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- École PolytechniqueFR315 papers
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- Laboratoire de Probabilités et Modèles AléatoiresFR17 papers
- Université Paris-SaclayFR16 papers
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- Laboratoire de Mathématiques Blaise PascalFR14 papers
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8 papers · 2 filters
Efficient Simulation of Hawkes Processes using their Affine Volterra Structure
Eduardo Abi Jaber, Elie Attal, Dimitri Sotnikov
We introduce a novel and efficient simulation scheme for Hawkes processes on a fixed time grid, leveraging their affine Volterra structure. The key idea is to first simulate the in…
Functional Limit Theorems for the range of stable random walks
Maxence Baccara
In this paper we establish Functional Limit Theorems for the range of random walks in that are in the domain of attraction of a non-degenerate -stable process in…
Long time behavior and Yaglom limit for real trait-structured Birth and Death Processes
Pierre Collet, Sylvie Méléard, Jaime San
In this article we study the long time behaviour of measure-valued birth and death processes in continuous time, where the dynamics between jumps are one-dimensional Markov process…
Exponentially Fading Memory Signature
Eduardo Abi Jaber, Dimitri Sotnikov
We introduce the exponentially fading memory (EFM) signature, a time-invariant transformation of an infinite (possibly rough) path that serves as a mean-reverting analogue of the c…
Weak solutions of Stochastic Volterra Equations in convex domains with general kernels
Eduardo Abi Jaber, Aurélien Alfonsi, Guillaume Szulda
We establish new weak existence results for -dimensional Stochastic Volterra Equations (SVEs) with continuous coefficients and possibly singular one-dimensional non-convolution…
Stochastic numerical approximation for nonlinear Fokker-Planck equations with singular kernels
Nicoleta Cazacu
This paper studies the convergence rate of the Euler-Maruyama scheme for systems of interacting particles used to approximate solutions of nonlinear Fokker-Planck equations with si…